In particular, it is known that material dispersion manifests through propagating pulses with frequency components
traveling at a different speed [1]}, [2]}: as the distance increases, the pulse becomes broader, hence the mathematical analysis
mainly concerns the study of the properties of the dispersion relation and the determination of decay properties
of various functional norms of the solutions of the initial value problem ([3]}).
In this paper we pursue this program (namely, understanding the dispersion relation of
propagating pulses and establishing regularity and decay estimates)
through a detailed study on how nonlocality influences the
dispersive behavior.
